Problem: Reduce to lowest terms: $- \dfrac{1}{4} \div \dfrac{4}{5} = {?}$
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $ \dfrac{4}{5}$ is $ \dfrac{5}{4}$ Therefore: $ - \dfrac{1}{4} \div \dfrac{4}{5} = - \dfrac{1}{4} \times \dfrac{5}{4} $ $ \phantom{- \dfrac{1}{4} \times \dfrac{5}{4}} = \dfrac{-1 \times 5}{4 \times 4} $ $ \phantom{- \dfrac{1}{4} \times \dfrac{5}{4}} = \dfrac{-5}{16} $